# Reynolds Number Calculator

Created by Gabriela Diaz
Last updated: Nov 30, 2022

Use the Reynolds number calculator to easily determine the Reynolds number of a fluid and identify if it's on a turbulent or laminar flow pattern.

• What is the Reynolds number?;
• The Reynolds number equation;
• How to calculate the Reynolds number; and
• Reynolds number for laminar flow and turbulent flow.

## What is the Reynolds number? – Reynolds number equation

Introduced in 1883 by the British engineer Osborne Reynolds, the Reynolds number is one of the most important dimensionless parameters used in fluid mechanics. This parameter describes the behavior of a Newtonian fluid by relating the inertial and viscous forces.

Inertial forces are related to the fluid's momentum. They resist changes in velocity and allow fluid motion to continue. Whereas viscous forces oppose to the motion and slow down the flow:

$\small Re = \cfrac{\text{inertial forces}}{\text{viscous forces}}$

Are you unsure of what momentum is or how to calculate it? Then Omni's might come in handy.

The inertial forces are dominant in turbulent flows. However, when the viscous forces govern, the flow is said to be laminar. The parameters affecting the inertia and viscosity of a fluid in motion are included in the Reynolds number formula:

$\small Re = \cfrac{\rho V L}{\mu} = \cfrac{VL}{\nu}$

where:

• $\rho$ - Density of the fluid in kg/m3 or lb/cu ft;
• $V$ - Velocity of the flow in m/s or ft/s;
• $L$ - Characteristic length of the flow in m or ft;
• $\mu$ - Dynamic viscosity of the fluid in kg/(m⋅s), or lb/(ft⋅s) or cP; and
• $\nu$ - Kinematic viscosity m2/s, or ft2/s or cSt.

🙋 Dynamic and kinematic viscosities are related via the density of the fluid, $\nu = \mu/\rho$, making it simple to convert from kinematic viscosity to dynamic viscosity.

For flow in a pipe, the Reynolds number equation can be expressed in terms of the volumetric flow rate Q as:

$\small Re = \cfrac{\rho \, Q \, D_H}{\mu \, A}$

where:

• $D_H$ - Hydraulic diameter of the pipe in m or ft; and
• $A$ - Cross-sectional area of the pipe in m2 of ft2.

## Reynolds number for laminar flow and turbulent flow – Laminar vs turbulent flow

The first step in studying a flow should be to calculate its Reynolds number. This value will define the flow pattern:

• Low values of Reynolds, $Re \leq 2100$ are associated with a laminar flow. This one is characterized by soft variations and slow and viscous flow. In this type of flow pattern, the predominant velocity and direction of the main flow coincide.

• High values of Reynolds number, $Re \geq 3000$, indicate turbulent flow. This flow type is dominated by inertial forces and is characterized by strong random fluctuations, vortices, eddies, and other instabilities.

• In between these two flow patterns, we find the transitional flow o, $2100 < Re < 3000$. This one combines laminar and turbulent flows. Turbulence in the center and laminar flow towards the pipe's edges.

The Reynolds number for laminar flow, transitional flow and turbulent flow are shown in the table below:

Reynolds number

Flow type

Re < 2100

Laminar

2100 < Re < 3000

Transitional

Re > 3000

Turbulent

## How to use the Reynolds number calculator

The Reynolds number calculator makes it simple to estimate the Reynolds number of a fluid and determines whether it is laminar or turbulent. To use this tool:

1. In the first section of the calculator, Flow parameters, input the fluid's velocity and characteristic length.
2. Below, you'll find the Fluid parameters section. Here you can choose from a list of different substances that already have charged their density and viscosities.
3. Once the flow and fluid parameters are defined, the calculator will display the Reynolds number and indicate the type of flow pattern, laminar, intermittent, or turbulent.

🙋 Can't find your substance on the list? You can manually input the density and viscosities of your custom fluid.

Gabriela Diaz
Flow parameters
Fluid velocity
ft/s
Characteristic linear dimension
ft
Fluid parameters
Substance
Custom ▾
Fluid density
lb/cu ft
Dynamic viscosity
oz
/(m*s)
Kinematic viscosity
ft²
/s
Reynolds number
Reynolds number
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